Hostname: page-component-76fb5796d-skm99 Total loading time: 0 Render date: 2024-04-29T15:10:35.261Z Has data issue: false hasContentIssue false

Dirichlet and Neumann boundary conditions for the p-Laplace operator: what is in between?

Published online by Cambridge University Press:  20 September 2012

Ralph Chill
Affiliation:
Laboratoire de Mathématiques et Applications de Metz, Université Paul Verlaine – Metz et CNRS, Bât. A, Ile du Saulcy, 57045 Metz Cedex 1, France (chill@univ-metz.fr)
Mahamadi Warma
Affiliation:
Department of Mathematics, Faculty of Natural Sciences, University of Puerto Rico (Rio Piedras Campus), PO Box 70377, San Juan, PR 00936-8377, USA (warma@uprrp.edu)

Abstract

Let p ∈ (1, ∞) and let Ω ⊆ ℝN be a bounded domain with Lipschitz continuous boundary. We characterize on L2(Ω) all order-preserving semigroups that are generated by convex, lower semicontinuous, local functionals and are sandwiched between the semigroups generated by the p-Laplace operator with Dirichlet and Neumann boundary conditions. We show that every such semigroup is generated by the p-Laplace operator with Robin-type boundary conditions.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 2012

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)